The atom coordinates in a unit cell whose origin has been shifted from 0
to ½a are equal to x - ½, compared to the earlier choice of origin :
To see how these origin choices effect the phases of reflections, consider the equation for the calculation
of the structure factor:
If the value of x after the origin shift by ½a (x - ½) is substituted into
the structure factor expression:
Thus, if the origin is shifted by ½a, reflections with even h index do not experience a change in phase;
relections with odd h change phase by 180° (e.g., from +Fhkl to -Fhkl).
For the eight reflection parity groups, the effect of changing the orign from 0, 0, 0 to ½a, 0, 0 is as
follows:
